Question

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg3. The doctor writes an exponential function to represent the situation. Which values should the doctor use for a and b in a function written in the form f(x) = abx, where f(x) represents the bone density after x years?

Answer 1

A=1500

B=0.97

Explanation:

Answer 2

The function f(x) is represented by:

`f(x)=1500(0.97)^x`

Hence, a=1500 and b=0.97

Explanation:

The patient currently has a bone density of 1,500 kg/mg^3.

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually.

This means that the bone density that is remaining is:

100-3=97%

which is also represented as: 97%=97/100=0.97

Hence, the function f(x) that represents the bone density after x years is represented by:

`f(x)=a(0.97)^x`

where a is the initial bone density which is given to be: 1500 kg/mg^3.

Hence, the function is:

`f(x)=1500(0.97)^x`